Performance comparison of the exact run-length distribution between the run sum X and EWMA X charts

• Main Authors: Chong, J.K., Teoh, W.L., Khoo, Michael B.C., Chong, Z.L., Teh, S.Y.
• Format: Article
• Language: English
• Published: Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia 2016
• Online Access: http://journalarticle.ukm.my/10200/1/jqma-12-1_2-paper2.pdf; http://journalarticle.ukm.my/10200/; http://www.ukm.my/jqma/jqma12_1_2a.html

The run sum (RS) X and exponentially weighted moving average (EWMA) X charts are very effective in detecting small and moderate process mean shifts. The design of the RS X and EWMA X charts based on the average run length (ARL) alone, can be misleading and confusing. This is due to the fact that the run-length distribution of a control chart is highly right-skewed when the process is in-control or slightly out-of-control; while that for the out-ofcontrol cases, the run-length distribution is almost symmetric. On the other hand, the percentiles of the run-length distribution provide the probability of getting a signal by a certain number of samples. This will benefit practitioners as the percentiles of the run-length distribution give comprehensive information regarding the behaviour of a control chart. Accordingly, this paper provides a thorough study of the run-length properties (ARL, standard deviation of the run length and percentiles of the run-length distribution) for the RS X and EWMA X charts. Comparative studies show that the EWMA X chart outperforms the RS X charts for detecting small mean shifts when all the control charts are optimized with respect to a small shift size. However, the RS X charts surpass the EWMA X chart for all sizes of mean shifts when all the control charts are optimized with respect to a large shift size.